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A270225 Lesser of twin primes where both primes are the sum of three squares.

%I A270225 #21 Sep 08 2022 08:46:16
%S A270225 3,11,17,41,59,107,137,179,227,281,347,419,521,569,617,641,659,809,
%T A270225 827,857,881,1019,1049,1091,1289,1427,1451,1481,1619,1667,1697,1721,
%U A270225 1787,1931,2027,2081,2129,2267,2339,2657,2729,2801,2969,3251,3257,3299,3329,3371,3467,3539
%N A270225 Lesser of twin primes where both primes are the sum of three squares.
%H A270225 Chai Wah Wu, <a href="/A270225/b270225.txt">Table of n, a(n) for n = 1..10000</a>
%F A270225 Primes p such that p == 1 or 3 mod 8 and p+2 is prime. - _Chai Wah Wu_, Jul 18 2016
%e A270225 3 is a term because 3 = 1^2 + 1^2 + 1^2 and 5 = 0^2 + 1^2 + 2^2.
%e A270225 17 is a term because 17 = 2^2 + 2^2 + 3^2 and 19 = 1^2 + 3^2 + 3^2.
%e A270225 41 is a term because 41 = 3^2 + 4^2 + 4^2 and 43 = 3^2 + 3^2 + 5^2.
%e A270225 59 is a term because 59 = 3^2 + 5^2 + 5^2 and 61 = 3^2 + 4^2 + 6^2.
%t A270225 Select[Prime[Range[500]], MemberQ[{1, 3}, Mod[#, 8]] && PrimeQ[# + 2] &] (* _Vincenzo Librandi_, Jul 18 2016 *)
%o A270225 (PARI) isA004215(n) = my(fouri, j) ; fouri=1 ; while( n >=7*fouri, if( n % fouri ==0, j= n/fouri-7 ; if( j % 8==0, return(1) ) ; ); fouri *= 4 ; ) ; return(0);
%o A270225 t(n, p=3) = { while( p+2 < (p=nextprime( p+1 )) || n-->0, ); p-2}
%o A270225 for(n=1, 1e2, if(!isA004215(t(n)) && !isA004215(t(n)+2), print1(t(n), ", ")));
%o A270225 (Python)
%o A270225 from sympy import prime, isprime
%o A270225 A270225_list = [p for p in (prime(i) for i in range(2,10**3)) if p % 8 not in {5,7} and isprime(p+2)] # _Chai Wah Wu_, Jul 18 2016
%o A270225 (Magma) [p: p in PrimesUpTo(4000) | IsPrime(p+2) and  p mod 8 in [1,3]]; // _Vincenzo Librandi_, Jul 18 2016
%Y A270225 Cf. A001359, A004215, A269840.
%K A270225 nonn
%O A270225 1,1
%A A270225 _Altug Alkan_, Mar 13 2016